By entanglement I mean some discreet event between two or more chains. Discreet means that I can say at what time the entanglement appeared, when did it disappear, which monomers of which chains have participated etc. This might be contrasted with the tube or mean field approach which assumes a more uniform and continuous entanglement field, created by many chains.
In order to see entanglement clearly in molecular dynamics (MD) simulations, we have to get rid of fast and rather chaotic motion on short time scales (below tau_e). One way to do this is by time and ensemble averaging. Here is the video of two chains selected from the melt, which are clearly entangled. The details of the simulations can be found in our paper, the chains are slightly semi-flexible (kb=3, N=100). What you see is not the chain position, but position of tube axis of each chain. The tube axis for each configuration is defined in the following way: I start m jobs (m=50 in this case) from the same initial configuration, run them for about tau_e, average position of each monomer over this time, and then average results over ensemble. The resulting tube axis is much much smoother then the chains themselves, and (hopefully) most of fast degrees of freedom are averaged out. This creates some very clear pictures - enjoy.
The green chain has its ends fixed, the purple is free. In the beginning the entanglement is very strong. At frame 19 it becomes weaker (look at the chain end), and at frame 53 they completely disentangle.
The disentanglement process is clearly illustrated by plotting the minimal distance between the tube axis of this pair of chains as a function of time. If the chains are entangled, it remains very small (of order one atom).
Surprisingly, this is not an exotic case. In this particular melt (with about 15-20 entanglements per chain according to usual definitions), almost each chain has such a strong or "double" entanglement. But of course they are not all the story - there are much more weaker entanglements.
In order to see entanglement clearly in molecular dynamics (MD) simulations, we have to get rid of fast and rather chaotic motion on short time scales (below tau_e). One way to do this is by time and ensemble averaging. Here is the video of two chains selected from the melt, which are clearly entangled. The details of the simulations can be found in our paper, the chains are slightly semi-flexible (kb=3, N=100). What you see is not the chain position, but position of tube axis of each chain. The tube axis for each configuration is defined in the following way: I start m jobs (m=50 in this case) from the same initial configuration, run them for about tau_e, average position of each monomer over this time, and then average results over ensemble. The resulting tube axis is much much smoother then the chains themselves, and (hopefully) most of fast degrees of freedom are averaged out. This creates some very clear pictures - enjoy.
The green chain has its ends fixed, the purple is free. In the beginning the entanglement is very strong. At frame 19 it becomes weaker (look at the chain end), and at frame 53 they completely disentangle.
The disentanglement process is clearly illustrated by plotting the minimal distance between the tube axis of this pair of chains as a function of time. If the chains are entangled, it remains very small (of order one atom).Surprisingly, this is not an exotic case. In this particular melt (with about 15-20 entanglements per chain according to usual definitions), almost each chain has such a strong or "double" entanglement. But of course they are not all the story - there are much more weaker entanglements.
3 comments:
The purple chain appears to have a self-entanglement, which disappears around about frame 6. But, if the green chain weren't there, the purple chain wouldn't be self-entangled. Curious.
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